Research on the synergy of the water–energy–food composite system in the Beijing–Tianjin–Hebei region

Water, energy, and food are fundamental and strategic resources essential for human survival and social development (Chang et al., 2016). Each of these resources relies on the other two, creating a complex interconnection. As the population grows and social development accelerates, the demand for water, energy, and food is expected to rise. It is projected that by 2030, the demand for these resources will increase to 40, 35, and 50%, respectively (Rzepczynski, 2014). Currently, issues such as climate change, ecological degradation, and other related challenges are escalating. Given the interconnected nature of these resources, studying them in isolation hinders the promotion of their coordinated development. Therefore, it is necessary to study the collaborative evolution of water, energy, and food as a composite system.

Since the water–energy–food (WEF) nexus was proposed, domestic and foreign scholars have conducted numerous studies on it from various perspectives, yielding abundant results. These include coupling coordination (Qi et al., 2022), risk (Ding & Chen, 2023), symbiosis (Fu et al., 2023), efficiency (Li & Huang, 2023), security (Nkiaka et al., 2021), and sustainability (Qian & Liang, 2021). Additionally, some scholars have explored the synergistic state of the system. It has been observed that the WEF system has been in a state of low cooperative evolution for an extended period, with a lack of synergy among some subsystems (Sun & Hao, 2022; Zhi et al., 2022). Studying the synergistic relationship of the WEF system is crucial as it can offer insights into the sustainable use of resources. Currently, scholars have conducted relevant studies on the synergy within the WEF system. Qualitatively, Gu et al. (2016) examined the synergy between energy consumption and water use from various angles. Zhang et al. (2013) proposed a synergistic strategy for water resources and food security based on the current development status of food and water resources in China. Srigiri & Dombrowsky (2022) conceptualized the WEF nexus as a multi-center system, comprehended the system's components and their logical interrelationships, and suggested achieving coordination through the collaborative integration of governance models. Quantitatively, on the one hand, some scholars have employed different methods to investigate the synergistic relationship of the system. Peng et al. (2017) introduced the synergetic theory, developed a WEF collaborative optimization model, and conducted an empirical analysis focusing on the Yellow River Basin to achieve an integrated and optimal layout of food production, energy development, and water resource deployment in the basin. Li et al. (2019) constructed a synergy network to explore the synergy effect within the urban WEF nexus in Shenzhen. Liu & Zhao (2022) utilized the improved Lotka-Volterra symbiosis model to evaluate the synergistic evolution status of the WEF nexus system in the Yellow River Basin. Ren et al. (2021) developed a regional WEF system collaborative development model based on complex adaptive system theory, co-evolution algorithm, and grey correlation analysis method, using Heilongjiang Province as a case study to empirically analyze the system's collaborative development. Conversely, some scholars primarily concentrate on the synergy of the WEF system in agricultural regions. Alam et al. (2019) employed remote sensing and hydrologic models to quantify the water and energy footprints of crops and analyzed their spatio-temporal changes in order to comprehensively evaluate the interaction of the WEF system in the Central Valley of California, aiding in better management of agricultural system development. Do et al. (2020) investigated the synergistic effects of the water–food–energy nexus in the Lancang-Mekong River Basin by employing an integrated hydro-economic optimization model, discovering that tradeoffs could be transformed into synergy, and dam operation could enhance irrigation water use and increase income from irrigated crops without significantly compromising hydropower production. Li et al. (2021) introduced a relative index of the water–energy–food system (WEF_RI) to analyze the synergies among water use, energy consumption, and food supply of different planting structures at the field scale. Additionally, synergies between resources have been explored to facilitate sustainable resource utilization. Radmehr et al. (2021) proposed a multi-criteria decision nonlinear programming method that not only optimizes resource allocation during food production but also assesses management policies for regional resource planning, offering decision-makers effective strategies for integrated planning for groundwater, energy, and food. Sargentis et al. (2021) examined the relationship between the development of photovoltaic power plants and food production in the Thessaly Plain, the largest agricultural area in Greece, aiming to uncover conflicts and synergies between the two, thereby mitigating negative impacts on the other three resources caused by the utilization of water, energy, food, and land. Caixeta et al. (2022) introduced a sustainability-focused excellence model that integrates WEF principles and the business excellence model to assist agro-industrial companies in managing tradeoffs and synergies between resources and transitioning toward enhancing sustainability. Kitessa et al. (2022) explored various feasible scenarios to enhance access and sustainability of resources in Addis Ababa city based on the WEF nexus modeling approach.

Most of the existing literature uses various models to study the synergy of the WEF system but rarely analyzes the degree of system synergy and the interaction between subsystems. As one of China's economic growth poles, the Beijing–Tianjin–Hebei region faces significant pressure in terms of water, energy, and food demand. These three regions have different levels of development, as well as varying natural resource endowments and usage structures (Liu et al., 2023). Therefore, this paper focuses on the Beijing–Tianjin–Hebei region as a case study and employs the composite system synergy degree model, the improved logistic model, and the panel vector autoregressive model (PVAR) to comprehensively analyze the synergy of the water–energy–food composite system (WEFCS). The aim is to provide insights for sustainable resource utilization and regional collaborative development.

This section consists of four parts: (1) status of regional resources; (2) data sources; (3) theoretical analysis, in which the collaborative framework of the WEFCS is constructed and the evaluation index system of synergy degree is established; and (4) research methods, including the entropy weight method used to determine the weight of indicators, the model to study the system's synergy degree, and the evolutionary model and panel vector autoregressive models to study subsystems.

Located in the heart of the Bohai Sea in Northeast China, the Beijing–Tianjin–Hebei region, which includes Beijing, Tianjin, and Hebei province, is an important economic and population agglomeration area in China. In 2021, the GDP of the Beijing–Tianjin–Hebei region reached 9.6 trillion yuan, accounting for 8.93% of the country's total. The total population reached 11.1 million, accounting for 7.8% of the total population. The Beijing–Tianjin–Hebei region is inherently deficient in water resources, with per capita water resources in 2021 only 357.83 m³, far lower than the national average of 2,098.5 m³. The total energy consumption was 478.938 million tons of standard coal, accounting for 9.14% of the total energy consumption of the country; China's total food production was 41.128 million tons, accounting for 6.02% of the country's total food production. Economic development and population agglomeration bring pressure on the WEF system, and the interrelated and restrictive characteristics of the three resources are gradually emerging. Considering only one resource will slow down the development of other resources. Therefore, it is of great significance to take the Beijing–Tianjin–Hebei region as an example to study the synergy of the WEFCS.

The research object of this paper is the Beijing–Tianjin–Hebei region. The data for each indicator are primarily sourced from the China Statistical Yearbook, China Energy Statistical Yearbook, Statistical Yearbook, and Water Resources Bulletin of Beijing, Tianjin, and Hebei from 2011 to 2021. Missing data have been substituted with linear trends. Additionally, to comprehensively evaluate the Beijing–Tianjin–Hebei region, the regional data has been obtained based on the average value of the three cities. The original data are provided in the Supplementary material.

As illustrated in Figure 1, the interdependence of resources is evident in various aspects: Hydropower generation and fossil energy extraction rely on water resources, essential for irrigation and crop growth. The management of water resources, sewage treatment, and recycling processes necessitate significant energy consumption. Additionally, energy is crucial for food production and processing. Food, a fundamental human necessity, serves as a cornerstone for water and energy security. Rice cultivation can contribute to water purification, while crops like corn, wheat, and cassava offer bioenergy resources. Nonetheless, there are adverse interactions among these resources. Water scarcity directly impacts food irrigation and growth, resulting in reduced food production. In areas where water is scarce, hydropower generation can be greatly affected, and some energy production methods, such as thermal power generation and shale gas extraction, can be limited. Wastewater and emissions from fossil energy extraction and processing can pollute water resources and soil, affecting the cultivation of food crops. Fertilizers, pesticides, and other chemicals used in food production can likewise pollute water resources. In summary, water, energy, and food promote and constrain each other, and the synergistic effect between their corresponding sequential parameters dominates the synergistic evolution of the composite system, which will gradually form a more advanced and stable structure.

With reference to the existing research results (Zhang et al., 2019; Zhi et al., 2020), and in accordance with the systematic, typical, scientific, and operational principles of index selection as well as the availability of data, the WEFCS synergy degree measurement indicator system is constructed. For the water and energy subsystems, indicators are selected from the aspects of supply, consumption, and pollution; for the food subsystem, indicators are selected from the two aspects of production and consumption. In addition, this paper adds the water resources consumed by energy and food production into the level of water consumption, the rural electricity consumption into the level of energy consumption, the irrigated area of cultivated land, and the total power of agricultural machinery into the dimension of food production. This reflects the cooperative correlation between subsystems. The specific synergy degree measurement indicator and weight are shown in Table 1.

The composite system S = (S1, S2, and S3) is defined, where S1 is the water subsystem, S2 is the energy subsystem, and S3 is the food subsystem. To eliminate the impact of dimension, the positive and negative indicators in the original data are standardized, as shown in the following formula:

In the formula, represents the value of indicator j of the standardized sample i, represents the initial value, and and represent the maximum and minimum values of indicator j.

The results of indicator weights are shown in Table 1.

Synergy ⁠, and the larger the value, the development of the system has reached high-quality synergy and long-term stability (Meng & Han, 1999), where ⁠. Formula (7) has two calculation criteria. One is based on the same time, and the synergy degree obtained is called the same base period synergy, which is used to describe the long-term evolution trend of the composite system. The other is based on the adjacent time, and the obtained synergy degree is the adjacent base period synergy degree, which is used to describe the development stability of the composite system. The judgment criteria of two different synergy degrees (Xia & He, 2018) are shown in Table 2, in which the grade of the same base period synergy degree is more detailed to comprehensively assess the synergy of the composite system.

Table 2

Synergy evaluation criteria.

Same base period synergy degree .	Synergy degree level .	Adjacent base period synergy degree .	Synergy degree stability .
−1cor − 0.66	Highly unsynergistic	−1cor0	Destabilizing synergy
−0.66cor − 0.33	Moderately unsynergistic	0cor0.2	Low stability synergy
−0.33cor0	Mildly unsynergistic	0.2cor0.6	Medium stability synergy
0cor0.33	Basic synergy	0.6cor1	High stability synergy
0.33cor0.66	Good synergy
0.66cor1	Quality synergy

Same base period synergy degree .	Synergy degree level .	Adjacent base period synergy degree .	Synergy degree stability .
−1cor − 0.66	Highly unsynergistic	−1cor0	Destabilizing synergy
−0.66cor − 0.33	Moderately unsynergistic	0cor0.2	Low stability synergy
−0.33cor0	Mildly unsynergistic	0.2cor0.6	Medium stability synergy
0cor0.33	Basic synergy	0.6cor1	High stability synergy
0.33cor0.66	Good synergy
0.66cor1	Quality synergy

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According to the Hurwitz criterion, the singular point is asymptotically stable when λ < 0. Therefore, when p < 0, q < 0, and r > 0, the point is stable.

Since Formula (9) is a nonlinear equation, in order to obtain the parameters of interaction between subsystems, this paper adopts an accelerated genetic algorithm (AGA), which has the characteristics of strong universality and stable global optimization ability. The general optimization problem is set as follows: ⁠, where (⁠⁠) is the initial change interval of ⁠, and f is the objective function. The new initial space of the algorithm is generated primarily based on the excellent individuals produced during the two iterations of the standard genetic algorithm. Subsequently, the variables are discretized and coded, and other steps are carried out sequentially to expedite the cycle (Jin et al., 2001) until the function value of the optimal individual is less than a certain specified value or the algorithm reaches a predetermined number of acceleration cycles. At this point, the best individual in the current group represents the outcome of AGA.

From the perspective of the same base period synergy degree, during 2012–2014, the same base period synergy degree of Beijing, Tianjin, and the Beijing–Tianjin–Hebei region showed a downward trend as a whole. During 2014–2021, the three regions all showed a ‘V’ shaped development stage, indicating that the WEFCS coordination was unstable during this period, especially in Tianjin. In Hebei province, the same base period synergy degree increased year by year after 2013, indicating that the synergistic interaction among subsystems in this region is improving and evolving toward a better state of synergy. From the perspective of the adjacent base period synergy degree, all of the four changes were between [−0.1, 0.1]. The adjacent base period synergy degree of WEFCS in 2013, 2014, and 2016 showed negative values, with Hebei province experiencing significant fluctuations in 2016, oscillating between positive and negative values. It is evident that the composite system oscillates between low stable and unstable co-evolution states for an extended period, possibly due to substantial changes in the order degree of subsystems over the years.

According to Figure 3, it can be seen that in terms of the order degree of the water resources subsystem, Beijing > Tianjin > the Beijing–Tianjin–Hebei region > Hebei province (see Figure 3(a)), with similar trends in the order degree of the water resources subsystems in Beijing, Tianjin, and the Beijing–Tianjin–Hebei region. The water resources subsystem of Hebei province exhibits the fastest development rate, and despite its outward expansion, it still lags behind the order degree of the water resources subsystem in the Beijing–Tianjin–Hebei region. This is attributed to the fact that Hebei is a major agricultural province, with an industrial structure dominated by the secondary industry, and that both agriculture and industry consume a large amount of water resources. It is evident that Hebei province should enhance the management of water resources. In terms of the order degree of the energy subsystem, Tianjin > Beijing > the Beijing–Tianjin–Hebei region > Hebei province (see Figure 3(b)). Despite the relatively low order degree of the energy subsystem in Hebei province, its development is quite rapid, while Beijing and the Beijing–Tianjin–Hebei region exhibit a relatively slower development of the energy subsystem. In terms of the order degree of the food subsystem (see Figure 3(c)), the region shows a slow but steady growth trend. Particularly, the order degree of the food subsystem is higher in Hebei province than in the other two cities.

Given that the collaborative state of regional WEFCS has not yet achieved a highly stable state, the water resources and energy subsystems are better developed in Beijing and Tianjin than in Hebei Province, while the food subsystem is better developed in Hebei Province than in Beijing and Tianjin. In order to realize the coordination between resources, the evolutionary model is further used to identify the correlation between the three subsystems. Combined with the order degree values of the subsystems above, the WEFCS evolutionary model is solved by an AGA, and the subsystems themselves and interaction parameters are obtained. The interaction types of subsystems in the Beijing–Tianjin–Hebei region are shown in Table 3.

Table 3

Synergistic evolution results in a steady state.

Subsystems .	.	.	.	Order degree .
Water	− 0.8848	− 1.3735	0.7414	1.2441
Energy	0.1592	0.6017	− 0.4924	1.0174
Food	− 0.0532	− 2.1642	2.1003	1.5556

Subsystems .	.	.	.	Order degree .
Water	− 0.8848	− 1.3735	0.7414	1.2441
Energy	0.1592	0.6017	− 0.4924	1.0174
Food	− 0.0532	− 2.1642	2.1003	1.5556

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Table 3 shows that ⁠, ⁠, and ⁠, which indicates that the energy subsystem is evolved in the steady state, while the water and food subsystems are degraded. For the water–energy system, where and ⁠, this indicates that the water resources and energy subsystems are interdependent. The clean energy production and utilization process has a relatively low demand for water resources, but in energy production processes such as fossil fuel extraction and thermal power generation, water scarcity may severely constrain energy production, leading to a decrease in the order degree of the energy subsystem. For the water–food system, where and ⁠, this means that the water resource and food subsystems are interdependent. Expansion of food cultivation area can increase the order degree of the food subsystem, but this also correspondingly increases the demand for water resources and reduces the order degree of the water subsystem. In turn, an increase in agricultural water use ensures the security of food supply and increases the order degree of the food subsystem. For the energy–food system, ⁠, ⁠, which shows that the energy and food subsystems are interdependent. The Beijing–Tianjin–Hebei region, with its geographical advantages in the North China Plain, has rich food resources and can provide biomass energy for the region, which is conducive to the orderly development of the energy subsystem. However, due to insufficient energy endowment, the region has certain limitations in energy supply, which affects the development of the food subsystem to some extent. Table 3 also indicates that the order degree of the water, energy, and food subsystems in a stable state reaches 1.2441, 1.0174, and 1.5556, respectively. This suggests that the water, energy, and food subsystems still require further improvement. Despite synergizing and competing with each other, the composite system ultimately evolves toward a stable structure.

In terms of the water–food system, Beijing has a mutually beneficial relationship (⁠⁠). Despite having a small cultivated land area, low grain output, and relatively scarce water resources, measures such as the South-to-North Water Diversion Project have enhanced water security for food production and alleviated the current water shortage situation. In addition, scientific and technological measures have further promoted the adjustment of agricultural industrial structure and promoted the development of green agriculture, which are conducive to the coordinated development of the water–food system. For both Tianjin and Hebei provinces, food is dependent on water resources (⁠⁠). Although the development of the food subsystem in Tianjin is relatively slow, the development of water resources in this region is restricted by agriculture as a major water consumer. Hebei province is one of the important grain production bases in our country. Food planting in this region not only consumes a large amount of water resources but also causes certain pollution to water resources and destroys the orderly development of the water resources subsystem. Through the construction of water conservancy projects such as reservoirs and embankments, the agricultural production water of the two places has been effectively guaranteed, and the development of the food subsystem has been promoted.

In terms of the energy–food system, there is competition between energy and food in the three regions of Beijing, Tianjin, and Hebei province (⁠⁠). The Beijing–Tianjin–Hebei region is located in the main food-producing area and has great potential for renewable energy development, especially in Hebei province, which contains natural gas, biomass, and other energy sources (Yan et al., 2021). The development and utilization of water resources are overloaded and their carrying capacity is insufficient, while food and energy rank first in the consumption of water resources at the same time. Due to the tight constraint of water resources, the conflict between the energy and food subsystems for water is relatively prominent, resulting in a restraining relationship between them.

There are various types of interactions between regional resource subsystems. To further investigate the development of the composite system, studying the dynamic interaction between subsystems is essential. Therefore, the PVAR model is chosen for analysis. Moreover, the first-order difference sequences of the water resources (WATER), energy (ENERGY), and food subsystems (FOOD) are represented as DWATER, DENERGY, and DFOOD, respectively.

Firstly, a unit root test is performed on the panel data to ensure model reliability and validity. In this paper, the Levin–Lin–Chu (LLC) test, augmented Dickey–Fuller (ADF) test, and Phillips–Perron (PP) test are selected to conduct a unit root test for the three variables, as shown in Table 4.

The results in Table 4 indicate that none of the three original variables pass the stability test. However, after the first-order difference processing, all variables pass the stability test at the 5% significance level.

Figure 5 illustrates that the inverses of the unit root modes all lie within the unit circle, indicating the stability of the constructed PVAR model.

Figure 6 illustrates that initially, the water, energy, and food subsystems all exhibit positive responses to respective impacts and reach their peaks. Over time, the responses of the three subsystems gradually diminish in different ways, indicating the future stable development of these subsystems. When the water subsystem experiences a standard deviation shock, the energy subsystem immediately shows a positive response, peaks, and then decreases to zero, suggesting a direct but limited influence from water to energy. The food subsystem initially shows no response, then responds positively and peaks in the second stage, followed by alternating between positive and negative responses before gradually approaching zero. This pattern indicates that the water resources subsystem has a delayed and complex effect on the food subsystem. When the energy subsystem is subjected to a standard deviation shock, the water resources subsystem initially does not respond. Subsequently, the second and third stages show significant positive and negative responses, respectively. After the sixth stage, the impact weakens to zero, indicating a lag and fluctuation in the impact of the energy subsystem on the water resources subsystem. The food subsystem initially responds negatively, then shifts to a positive response in the fourth stage, eventually converging to zero after fluctuations. This demonstrates the intricate interdependence between the energy subsystem and the food subsystem. When the food subsystem experiences a standard deviation shock, the water and energy subsystems are initially unresponsive. Subsequently, the water subsystem is negatively affected in the third stage, with a brief positive response in the fifth stage. However, this positive effect diminishes over time and turns negative again in the seventh stage. The energy subsystem exhibits a rapid increase in positive response in the second stage, followed by fluctuation until it reaches zero. This suggests that the food subsystem has a delayed and complex influence on the water and energy subsystems, with the water subsystem being more significantly affected.

Compared with previous studies (Zhang et al., 2019; Liu et al., 2023), this paper aims to investigate the development trend of the WEFCS and the interaction of internal subsystems from the perspective of synergy. Based on the evaluation results of synergy degree and order degree, from 2011 to 2021, the synergy degree of the composite system in the Beijing–Tianjin–Hebei region remains at a basic level, while the order degree of the water, energy, and food subsystems all exhibit an increasing trend. This is consistent with the findings of Zhi et al. (2022). Furthermore, regarding the types of subsystem interactions, in comparison with Sun & Hao (2022), both studies conclude that there are synergistic, dependent, and competitive relationships within the internal subsystems. Additionally, this paper reveals that for a short period, the energy subsystem has a negative impact on the food subsystem, while the food subsystem has a positive effect on the energy subsystem. Zhang et al. (2022) demonstrated that energy consistently displayed a negative response to food shocks. Despite some discrepancies between our findings and those of other studies, these variations may highlight issues that have been overlooked or underemphasized in previous research, aiding in the identification of potential challenges.

The composite system is complex and needs to consider the impact of future policy or environmental changes. Firstly, if the government further strengthens the management of water resources, such as widely promoting water-saving irrigation technology and strengthening water pollution control, the Beijing–Tianjin–Hebei region is expected to improve the efficiency of water use. Wen et al. (2022) found that improving water use efficiency in agriculture and industry could effectively save water resources and thus alleviate the pressure of water shortages. Feng et al. (2023) pointed out the importance of strengthening water pollution management in the context of global warming. These measures will greatly facilitate the optimal use of regional water resources. Secondly, if the region vigorously develops clean energy, the security and stability of the energy subsystem will be improved. Sun et al. (2018) predicted that by 2030, the regional energy structure would tend to be low-carbon, cleaner, and electrified. This transition can significantly reduce air pollutant emissions from fossil fuel combustion (Bo et al., 2023) and water utilization, playing a key role in the synergy of the WEFCS. Thirdly, if the government further optimizes the layout of food production and strengthens research in agricultural science and technology, food production will be further improved. Improving irrigation systems and planting drought-resistant crops have been shown to be effective in reducing agricultural water demand (Opoku et al., 2022). Considering the severe water challenges faced by the Beijing–Tianjin–Hebei region as a major food-producing area (Wang et al., 2022), realizing synergistic development of water resources and food production is key to alleviating the pressure.

This paper mainly uses the synergy model, evolutionary model, and panel vector autoregression model to study the synergy of the composite system, and these assessment models can be applied to complex systems involving multiple factors in other regions. The Beijing–Tianjin–Hebei region differs from other regions in terms of resource endowment, economic development, and demographics, so the policies proposed in this study are not directly applicable to other regions, but can provide valuable references for them. As a priority area for synergistic development, the Beijing–Tianjin–Hebei region is expected to receive more resources, which provides the possibility for policy implementation. However, resource management involves the interests of many parties, this may also affect the implementation of policies. Specifically for individuals or enterprises, there may still be opposition to the new policy.

Based on the above analysis, policy recommendations are put forward: as the synergy degree of the composite system has not yet reached a high level, the sector should formulate unified policy planning for water, energy, and food, and establish a sound early warning mechanism for the risks of the composite system. The region should strengthen cooperation, establish an information-sharing platform, and enhance cross-regional cooperation in major infrastructure construction and environmental protection. In regions where water and energy are interdependent, the government should increase efforts in researching, developing, and applying new energy technologies and promoting the use of clean energy in energy production. They should further promote water-saving technologies and take strict measures to control sewage discharge. In areas where water and food are interdependent, agricultural water-saving technologies, such as sprinklers and drip irrigation, should be vigorously promoted. The strategy of ‘food crop production strategy based on farmland management and technological application’ should be implemented to improve comprehensive agricultural production capacity. Regarding the dependence or competition between energy and food, under the constraints of water, land, and other resources, the government should rationally plan the layout of the food and energy industries and promote energy utilization technologies for agricultural waste.

This paper explores the synergy of the WEFCS, but there are still deficiencies. Firstly, missing data and data anomalies have some impact on the acquisition of indicators, thus affecting the assessment of synergy degree, which can be solved by considering new techniques in the future. Then, it mainly focuses on the empirical analysis of the synergy of the system and does not explore the advantages and disadvantages of different methods in the synergy analysis, which can be considered for comparative analysis with other models in the future. Finally, the long-term impacts of the synergistic relationship are complex, and further research will consider collecting data over a longer period of time, strengthening cooperation with related disciplines of geography, environmental science, and economics to jointly explore the long-term impacts, as well as examining the impact of external factors such as population growth, economic development, and urbanization.

Expanding from the system and subsystem perspectives, this paper analyzes the synergy of the WEFCS in the Beijing–Tianjin–Hebei region from 2011 to 2021. The results indicate that regional WEFCS synergy is low and unstable during the study period, and the synergy degree of the respective composite system in the three regions fluctuates and changes with instability by region. At the subsystem level, the development of the food subsystem lags behind in the region, while the water resource subsystem performs well in Beijing, the energy subsystem dominates in Tianjin, and the food subsystem develops more prominently in Hebei province. Additionally, there are obvious dependencies among different subsystems in the Beijing–Tianjin–Hebei region as a whole. For each region, some subsystem combinations such as the water–food system in Beijing and the water–energy system in Tianjin show mutually beneficial synergistic relationships, while other subsystem combinations show dependence or competition relationships. Moreover, the interactions among regional subsystems include not only direct effects, such as the positive promotion of the water resources subsystem on the energy subsystem and the negative restriction of the energy subsystem on the food subsystem but also numerous delayed and complex effects, in which the water resources subsystem is particularly affected by the food subsystem. These findings provide important references for future resource management and policy formulation in the Beijing–Tianjin–Hebei region and help to promote the sustainable development of the regional WEFCS.

This research was funded by the 2023 Funding Project from the Key Research Bases of Humanities and Social Sciences of Higher Education Institutions in Hebei Province (Grant No. JJ2311) and the research project of Hebei Province's social science development from Hebei Federation of Social Science Associations (Grant Nos. 20230202063 and 20220202459).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.